Neuromorphic systems, which emulate neural functionalities of a human brain, are considered to be an attractive next‐generation computing approach, with advantages of high energy efficiency and fast computing speed. After these neuromorphic systems are proposed, it is demonstrated that artificial synapses and neurons can mimic neural functions of biological synapses and neurons. However, since the neuromorphic functionalities are highly related to the surface properties of materials, bulk material‐based neuromorphic devices suffer from uncontrollable defects at surfaces and strong scattering caused by dangling bonds. Therefore, 2D materials which have dangling‐bond‐free surfaces and excellent crystallinity have emerged as promising candidates for neuromorphic computing hardware. First, the fundamental synaptic behavior is reviewed, such as synaptic plasticity and learning rule, and requirements of artificial synapses to emulate biological synapses. In addition, an overview of recent advances on 2D materials‐based synaptic devices is summarized by categorizing these into various working principles of artificial synapses. Second, the compulsory behavior and requirements of artificial neurons such as the all‐or‐nothing law and refractory periods to simulate a spike neural network are described, and the implementation of 2D materials‐based artificial neurons to date is reviewed. Finally, future challenges and outlooks of 2D materials‐based neuromorphic devices are discussed.